Add The Following Expressions:$\left(8a^2 + 8\right) + \left(2a^2 + 9a + 3\right$\]

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will focus on adding two algebraic expressions, $\left(8a^2 + 8\right) + \left(2a^2 + 9a + 3\right)$. We will break down the process into manageable steps, making it easier to understand and apply.

Understanding the Problem

The given problem involves adding two algebraic expressions. The first expression is $\left(8a^2 + 8\right)$, and the second expression is $\left(2a^2 + 9a + 3\right)$. Our goal is to simplify the resulting expression by combining like terms.

Step 1: Distribute the Addition Operation

To add the two expressions, we need to distribute the addition operation to each term inside the parentheses. This means we will add the corresponding terms from each expression.

\left(8a^2 + 8\right) + \left(2a^2 + 9a + 3\right)
= 8a^2 + 8 + 2a^2 + 9a + 3

Step 2: Combine Like Terms

Now that we have distributed the addition operation, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two terms with the variable $a^2$ and two terms with the variable $a$.

8a^2 + 8 + 2a^2 + 9a + 3
= (8a^2 + 2a^2) + (9a) + (8 + 3)

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by evaluating the expressions inside the parentheses.

(8a^2 + 2a^2) + (9a) + (8 + 3)
= 10a^2 + 9a + 11

Conclusion

In this article, we have simplified the algebraic expression $\left(8a^2 + 8\right) + \left(2a^2 + 9a + 3\right)$ by distributing the addition operation and combining like terms. The resulting expression is $10a^2 + 9a + 11$. This process demonstrates the importance of simplifying algebraic expressions in solving equations and inequalities.

Tips and Tricks

• When adding algebraic expressions, make sure to distribute the addition operation to each term inside the parentheses.
• Combine like terms by adding or subtracting the coefficients of the same variable raised to the same power.
• Simplify the expression by evaluating the expressions inside the parentheses.

Common Mistakes

• Failing to distribute the addition operation to each term inside the parentheses.
• Not combining like terms.
• Not simplifying the expression by evaluating the expressions inside the parentheses.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, simplifying algebraic expressions can help us solve equations that describe the motion of objects. In engineering, simplifying algebraic expressions can help us design and optimize systems. In economics, simplifying algebraic expressions can help us model and analyze economic systems.

Final Thoughts

Simplifying algebraic expressions is a crucial skill that helps us solve equations and inequalities. By following the steps outlined in this article, we can simplify complex algebraic expressions and make them more manageable. Remember to distribute the addition operation, combine like terms, and simplify the expression by evaluating the expressions inside the parentheses. With practice and patience, you will become proficient in simplifying algebraic expressions and apply this skill to real-world problems.